Transmission power control has paramount importance in the design of energy-efficient wireless sensor networks (WSNs). In this paper, we systematically explore the effects of various transmission power control strategies on WSN lifetime with an emphasis on discretization of power levels and strategies for transmission power assignment. We investigate the effects of the granularity of power levels on energy dissipation characteristics through a linear programming framework by modifying a well known and heavily utilized continuous transmission power model (HCB model). We also investigate various transmission power assignment strategies by using two sets of experimental data on Mica motes. A novel family of mathematical programming models are developed to analyze the performance of these strategies. Bandwidth requirements of the proposed transmission power assignment strategies are also investigated. Numerical analysis of our models are performed to characterize the effects of various design parameters and to compare the relative performance of transmission power assignment strategies. Our results show that the granularity of discrete energy consumption has a profound impact on WSN lifetime, furthermore, more fine-grained control of transmission power (i.e., link level control) can extend network lifetime up to 20% in comparison to optimally-assigned network-level single transmission power.